Algebraic and Geometric Methods in Enumerative Combinatorics
by Federico Ardila
Publisher: arXiv 2014
Number of pages: 143
The guiding principle was to focus on algebraic and geometric techniques that are useful towards the solution of enumerative problems. The main goal of this survey is to state clearly and concisely some of the most useful tools in algebraic and geometric enumeration, and to give many examples that quickly and concretely illustrate how to put these tools to use.
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by Richard P. Stanley - MIT
Contents: Walks in graphs; Cubes and the Radon transform; Random walks; The Sperner property; Group actions on boolean algebras; Young diagrams and q-binomial coefficients; Enumeration under group action; A glimpse of Young tableaux; etc.
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In 1998, Gian-Carlo Rota gave his famous course at MIT. John N. Guidi took notes in a verbatim manner conveying the substance of the course. Topics covered included sets, relations, enumeration, order, matching, matroids, and geometric probability.
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Topics covered in this book include fundamental of mathematical combinatorics, differential Smarandache n-manifolds, combinatorial or differentiable manifolds and submanifolds, Lie multi-groups, combinatorial principal fiber bundles, etc.
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This introduction to combinatorics, the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. Some ability to construct proofs is assumed.